Dimension dependent hypercontractivity for Gaussian kernels

被引：15

作者：

Bakry, Dominique ^{[2
]}

Bolley, Francois ^{[1
]}

Gentil, Ivan ^{[3
]}

机构：

[1] Univ Paris 09, CEREMADE, F-75116 Paris, France

[2] Univ Toulouse, Inst Math Toulouse, Univ Toulouse 3, F-31062 Toulouse, France

[3] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2012年 / 154卷 / 3-4期

关键词：

Hypercontractive bound; Diffusion semigroup; Logarithmic Sobolev inequality; Curvature-dimension criterion; Transportation inequality; LOGARITHMIC SOBOLEV INEQUALITIES; TRANSPORTATION COST;

D O I：

10.1007/s00440-011-0387-y

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imply classical bounds on the Ornstein-Uhlenbeck semigroup and a dimensional and refined (transportation) Talagrand inequality when applied to the Hamilton-Jacobi equation. Hypercontractive bounds on the Ornstein-Uhlenbeck semigroup driven by a non-diffusive L,vy semigroup are also investigated. Curvature-dimension criteria are the main tool in the analysis.

引用

页码：845 / 874

页数：30

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